The majority of current mechanical watches are fitted with a spring balance and a Swiss anchor escapement mechanism. The spring balance forms the time base of the watch. This is also called a resonator.
The escapement itself performs two main functions:                maintaining the reciprocating movements of the resonator;        counting these reciprocating movements.        
In addition to these two main functions the escapement must be robust, impact-resistant and prevent jamming of the movement (overbanking).
The Swiss anchor escapement mechanism has a low energy efficiency (about 30%). This low efficiency results from the fact that the movements of the escapement are intermittent, that there are drops or backlashes to adapt to machining errors, and also from the fact that several components transmit their movement via inclined planes that run up against one another.
An inertial element, a guide arrangement and an elastic restoring element are needed to form a mechanical resonator. Traditionally, a spiral spring plays the role of elastic restoring element for the inertial element belonging to a balance. This balance is rotatably guided by pivots, which turn in smooth ruby bearings. This causes friction and therefore energy losses and disruptions to operation, which depend on positions and which one seeks to remove. The losses are characterised by the quality factor Q. The aim is to maximise this factor Q.
Patent application EP2847547 in the name of Montres BREGUET describes a mechanism for regulating the pivoting rate around a first pivot axis of a wheel train, in particular a striking mechanism, having an inertia block that pivots around a second pivot axis parallel to the first. The regulator has means for restoring the inertia block towards the first axis. When the wheel train pivots at a rate below a reference rate, the inertia block remains confined in a first revolution space around the first axis. When this wheel train pivots at a rate above the reference rate, the inertia block enters a second revolution space around the first axis, which is adjacent to and outside the first revolution space, and a peripheral portion of the inertia block cooperates in this second revolution space with regulation means arranged to cause the braking of the wheel train and bring its pivoting rate back to the reference rate, and to dissipate the excess energy. In particular, the wheel train is subjected to a braking torque by Foucault currents.
Patent application EP14184155 in the name of ETA Manufacture Horlogère Suisse describes a clockmaking regulator mechanism having the following that are movably mounted at least to pivot in relation to a plate: an escape wheel arranged to receive a driving torque via a train and a first oscillator having a first rigid structure connected to the plate by first elastic restoring means. This regulator mechanism has a second oscillator having a second rigid structure connected to the first rigid structure by second elastic restoring means, and that has guide means arranged to cooperate with complementary guide means belonging to the escape wheel that synchronise the first oscillator and the second oscillator with the train.
Patent application EP15153657 in the name of ETA Manufacture Horlogère Suisse describes a clockmaking oscillator having a structure and separate primary resonators, which are temporally and geometrically out of phase, each having a mass restored towards the structure by an elastic restoring means. This clockmaking oscillator has coupling means for interaction of the primary resonators that have driving means to cause a wheel train to move that has drive and guide means arranged to drive and guide a control means articulated to transmission means that are each articulated at a distance from the control means with a mass of a primary resonator, and the primary resonators and the wheel train are arranged so that the articulation axes of any two of the primary resonators and the articulation axis of the control means are never coplanar.
Patent application PCT/EP2015/065434 in the name of The Swatch Group Research & Development Ltd describes a clockmaking assembly having a combined resonator with improved isochronism to at least two degrees of freedom, which has a first linear or rotary oscillator of reduced amplitude in a first direction, in relation to which a second linear or rotary oscillator of reduced amplitude in a second direction substantially orthogonal to the first direction oscillates, this second oscillator comprises a second support mass of a sliding block. This clockmaking assembly has a wheel train arranged for the application of a torque of the resonator, wherein this wheel train has a groove, into which the sliding block slides with minimum play. This sliding block is arranged to at least either follow the curve of the groove when it has one or frictionally rub in the groove, or push back the inside lateral surfaces belonging to the groove by magnetised or electrified surfaces belonging to the sliding block.
Document FR630831A in the name of Schieferstein describes a process and a device for the transmission of power between mechanical systems or for the control of mechanical systems where two oscillating movements of flexible mechanisms forming an appropriate angle between them act on one another, so that an oscillation is produced that takes place along a closed curve and which in the aim of force transmission or of control is loosely coupled in accordance with a rotational movement. The restoring means are attached to the plate. The connecting element between the masses are elastic and consequently do not constitute kinematic linkages.
Document EP3095011A2 and document WO2015/104962 in the name of EPFL describe a mechanical isotropic harmonic oscillator comprising at least one two degrees of freedom linkage supporting an orbiting mass with respect to a fixed base with springs having isotropic and linear restoring properties. More specifically, a plane spring stage forms a two degree of freedom linkage actuating a purely translational movement of the orbiting mass so that the mass is displaced along its orbit while maintaining a fixed orientation. In a variant each spring stage comprises at least two parallel springs. The springs or other associated restoring means are again attached to the plate here.
When a mass guided to rotate around a fixed axis and connected to this axis by a radial linear restoring spring is driven to rotate by a grooved wheel, if a pin running in this groove is fixed to the mass and if this mass is point-form, its trajectories are ellipses or circles and are all isochronic. If the mass has a rotational inertia, then only the circular trajectories are isochronic. Particular conditions that are quite difficult to fine tune can allow the trajectories on circles to be stabilised, the resonator will then remain isochronic as a function of the driving torque of the wheel.